### All GMAT Math Resources

## Example Questions

### Example Question #58 : Quadrilaterals

Note: Figure NOT drawn to scale

Refer to the above figure, which shows Square and Square . The ratio of to is 13 to 2. What is the ratio of the area of Square to that of Square ?

**Possible Answers:**

**Correct answer:**

To make this easier, assume that and - the reasoning generalizes. Then Square has sidelength 15 and area . The sidelength of Square , each side being a hypotenuse of a right triangle with legs 2 and 13, is

.

The square of this, 173, is the area of Square .

The ratio is .

### Example Question #59 : Quadrilaterals

Note: Figure NOT drawn to scale

Refer to the above figure, which shows Square and Square . The ratio of to is 7 to 1.

Which of these responses comes closest to what percent the area of Square is of that of Square ?

**Possible Answers:**

**Correct answer:**

To make this easier, assume that and ; the results generalize.

Each side of Square has length 8, so the area of Square is 64.

Each of the four right triangles has legs 7 and 1, so each has area ; Square has area four times this subtracted from the area of Square , or

.

The area of Square is

of that of Square .

Of the five choices, 80% comes closest.

### Example Question #61 : Quadrilaterals

The perimeter of a square is the same as the circumference of a circle with area 100. What is the area of the square?

**Possible Answers:**

**Correct answer:**

The formula for the area of a circle is

.

If the area is 100, the radius is as follows:

The circle has circumference times its radius, or

This is also the perimeter of the square, so the sidelength of the square is one-fourth this, or

The area of the square is the square of this, or

### Example Question #62 : Quadrilaterals

The perimeter of a square is the same as the circumference of a circle with radius 8. What is the area of the square?

**Possible Answers:**

The correct answer is not among the other choices.

**Correct answer:**

A circle with radius 8 has as its circumference times this, or

.

This is also the perimeter of the square, so the sidelength is one fourth of this, or

.

The area is the square of this, or

.

### Example Question #63 : Quadrilaterals

The perimeter of a square is the same as the length of the hypotenuse of a right triangle with legs 8 and 12. What is the area of the square?

**Possible Answers:**

The correct answer is not among the other responses.

**Correct answer:**

The length of the hypotenuse of a right triangle with legs 8 and 12 can be determined using the Pythagorean Theorem:

Since this is also the perimeter of the square, its sidelength is one fourth of this, or

The area of the square is the square of this sidelength, or

### Example Question #21 : Squares

If the perimeter of a square is , what is its area?

**Possible Answers:**

**Correct answer:**

The perimeter of a square, and any shape for that matter, is found by adding up all the exterior sides. Since all sides are equal in a square, we can say:

where represents the length of a side

We can solve for the side length using the information provided:

The area of a square is found by squaring the side length:

### Example Question #65 : Quadrilaterals

The perimeter of a square is . Give its area.

**Possible Answers:**

**Correct answer:**

The length of one side of a square is the perimeter divided by 4:

Square this to get the area: